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Answer :
To simplify the expression [tex]\( 14 x^5(13 x^2 + 13 x^5) \)[/tex], let's break it down step-by-step:
1. Distribute the [tex]\( 14 x^5 \)[/tex] inside the parentheses:
We have [tex]\( 14 x^5 \)[/tex] multiplying each term inside the parentheses [tex]\( (13 x^2 + 13 x^5) \)[/tex]. Use the distributive property:
[tex]\[
14 x^5 \cdot 13 x^2 + 14 x^5 \cdot 13 x^5
\][/tex]
2. Multiply the coefficients and the powers of [tex]\( x \)[/tex] separately:
- For the first term: [tex]\( 14 \cdot 13 = 182 \)[/tex] and [tex]\( x^5 \cdot x^2 = x^{5+2} = x^7 \)[/tex]
- For the second term: [tex]\( 14 \cdot 13 = 182 \)[/tex] and [tex]\( x^5 \cdot x^5 = x^{5+5} = x^{10} \)[/tex]
3. Combine the simplified terms:
The first term is [tex]\( 182 x^7 \)[/tex] and the second term is [tex]\( 182 x^{10} \)[/tex].
So, the simplified expression is:
[tex]\[
182 x^7 + 182 x^{10}
\][/tex]
The correct answer that matches our simplified expression is:
c. [tex]\( 182 x^7 + 182 x^{10} \)[/tex]
1. Distribute the [tex]\( 14 x^5 \)[/tex] inside the parentheses:
We have [tex]\( 14 x^5 \)[/tex] multiplying each term inside the parentheses [tex]\( (13 x^2 + 13 x^5) \)[/tex]. Use the distributive property:
[tex]\[
14 x^5 \cdot 13 x^2 + 14 x^5 \cdot 13 x^5
\][/tex]
2. Multiply the coefficients and the powers of [tex]\( x \)[/tex] separately:
- For the first term: [tex]\( 14 \cdot 13 = 182 \)[/tex] and [tex]\( x^5 \cdot x^2 = x^{5+2} = x^7 \)[/tex]
- For the second term: [tex]\( 14 \cdot 13 = 182 \)[/tex] and [tex]\( x^5 \cdot x^5 = x^{5+5} = x^{10} \)[/tex]
3. Combine the simplified terms:
The first term is [tex]\( 182 x^7 \)[/tex] and the second term is [tex]\( 182 x^{10} \)[/tex].
So, the simplified expression is:
[tex]\[
182 x^7 + 182 x^{10}
\][/tex]
The correct answer that matches our simplified expression is:
c. [tex]\( 182 x^7 + 182 x^{10} \)[/tex]
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